Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems
This comprehensive introduction to the calculus of variations and its main principles also presents their real-life applications in various contexts: mathematical physics, differential geometry, and optimization in economics. Based on the authors' original work, it provides an overview of the f...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2010
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| Series: | Encyclopedia of mathematics and its applications
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| Subjects: | |
| Online Access: | |
| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- Part I. Variational Principles in Mathematical Physics: 1. Variational principles
- 2. Variational inequalities
- 3. Nonlinear eigenvalue problems
- 4. Elliptic systems of gradient type
- 5. Systems with arbitrary growth nonlinearities
- 6. Scalar field systems
- 7. Competition phenomena in Dirichlet problems
- 8. Problems to Part I
- Part II. Variational Principles in Geometry: 9. Sublinear problems on Riemannian manifolds
- 10. Asymptotically critical problems on spheres
- 11. Equations with critical exponent
- 12. Problems to Part II
- Part III. Variational Principles in Economics: 13. Mathematical preliminaries
- 14. Minimization of cost-functions on manifolds
- 15. Best approximation problems on manifolds
- 16. A variational approach to Nash equilibria
- 17. Problems to Part III; Appendix A. Elements of convex analysis; Appendix B. Function spaces; Appendix C. Category and genus; Appendix D. Clarke and Degiovanni gradients; Appendix E. Elements of set-valued analysis